Unsolved for 500 Years: Researchers Crack Leonardo da Vinci’s Paradox

Bubbles Red Arrow

Five centuries ago, Leonardo da Vinci observed air bubbles deviating from a straight path in a zigzag or spiral motion. However, the cause of this periodic motion remained unknown until now.

Researchers from the universities of Seville and Bristol have solved the mystery surrounding the unsteady path of an air bubble rising in water.

Professors Miguel Ángel Herrada of the University of Seville and Jens G. Eggers of the University of Bristol have uncovered a mechanism that explains the erratic movement of bubbles rising in water. The findings, published in the prestigious journal Proceedings of the National Academy of Sciences, could provide insights into the behavior of particles that fall between solid and gas states.

Leonardo da Vinci observed five centuries ago that air bubbles, if big enough, periodically deviate in a zigzag or spiral from a straight-line movement. However, no quantitative description of the phenomenon or physical mechanism to explain this periodic motion had ever been found.

Leonardo’s Sketch Showing the Spiral Motion of an Ascending Bubble

Leonardo’s sketch showing the spiral motion of an ascending bubble (from his manuscript known as the Codex Leicester). Credit: Universidad de Sevilla

The authors of this new paper have developed a numerical discretization technique to characterize precisely the bubble’s air-water interface, which enables them to simulate its motion and explore its stability. Their simulations closely match high-precision measurements of unsteady bubble motion and show that bubbles deviate from a straight trajectory in water when their spherical radius exceeds 0.926 millimeters, a result within 2% of experimental values obtained with ultrapure water in the 90s.

The researchers propose a mechanism for the instability of the bubble trajectory whereby periodic tilting of the bubble changes its curvature, thus affecting the upward velocity and causing a wobble in the bubble’s trajectory, tilting up the side of the bubble whose curvature has increased. Then, as the fluid moves faster and the fluid pressure falls around the high-curvature surface, the pressure imbalance returns the bubble to its original position, restarting the periodic cycle.

Reference: “Path instability of an air bubble rising in water” by Miguel A. Herrada and Jens G. Eggers, 17 January 2023, Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2216830120

21 Comments on "Unsolved for 500 Years: Researchers Crack Leonardo da Vinci’s Paradox"

  1. I recall a few days in school when I (might have been) pondering a similar problem involving carbonated soda. The result of those sessions was an instructor asking me, in a loud voice if “I was on drugs?”

  2. TRULYTRUE TRUE, I agree with you completely absolutely and I agree with your perspective

    TRULYTRUE TRUE, this is an easy thing to crack, the reason for the movement is, the greater universe is moving in a BRAIDED MOTION, thus, everything inside is also condemned to this LONG DRAWN OUT PERPETUAL MOTION.

    • I do not think it is condemnation, and seems braided – I think it is mostly currents of vortex shedding of which you speak.

  3. Excellent article regarding new scientific explanation and I would have liked a diagramatic representation of this new science.

  4. When water goes down a drain it turns the same direction so maybe when air rises in water their is a similar force but different reactions that are unrelated by action cause it’s a different dynamic

  5. Excellent

  6. I am so relieved they were able to solve this “paradox”. While spending no less than a couple of hundred thousands dollars to do so, I’m sure. Finally, all is right with the world, and we can live better lives knowing that this mystery has been laid to rest.

    • From Maxwell to Tesla,everything is a waste of money until it isn’t !!

    • Reading your comment made me laugh. Sadly there’s no like button to highlight this. 😂

      • Maybe this can be explained, or already has been, but why do we even have bubble(s)? As in plural…

        If a gas is being expelled at a constant pressure, displacing the liquid, why is there not ONE bubble?

  7. We used to see this phenomena when we exhaled while diving underwater.

  8. Why….all the things to figure out and this is it. Such a waste of money and expertise.

    • I agree.

    • One should never deem something useless and a waste of money and expertise just because you don’t see a direct application for it. Not going to act like I can think of any practical use for this knowledge but I’m willing to bet that even something as seemingly useless as bubble movement could potentially hold the key to future developments that change the world. Don’t undervalue the small stuff, remember that’s what the big stuff is made out of.. No such thing as useless knowledge in my opinion.

  9. Michael G P McCabe | February 6, 2023 at 5:32 pm | Reply

    Not necessarily wasted time and money. Think of the diffusion of asymmetric small particles going through cell cytoplasm, like messenger RNA en route from the nucleus to the cytoplasmic ribosomes . I made a model of such a system 40 odd years ago, and observed that it would inevitably spiral, but still maintain its true direction.(see: Should reptation Theory for the Migration of linear DNA through Gels include screwing? J Journal of Theoretical Biology (1984), vol107,pages165-167,

  10. From Maxwell to Tesla,everything is a waste of money until it isn’t !!

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  13. So this deviation from straight line will not happen If the bubble is engulfed in a hard ball, like pingpong ball, am i right?
    Well these phenomenons are multifactoral, like movement of a smoke particle, no math can predict. Temperature, viscosity , convectional currents etc.

  14. Going back to the waste of time and money conversation, if I were to compare complaints between the “science of bubbles” project and what CERN is doing with the Particle Collider, in my opinion, CERN wins hands down. Only they’re using our money to their favor in an extremely dangerous way.

  15. … in a light of statement> “every thing is predictable…

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